Horse friends - math puzzle

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Three horses are standing in a triangular field, which is exactly 100
yards on each side. One horse stands at each corner; and simultaneously
all three set off running. Each horse runs after the horse in the
adjacent corner on his left, thus following a curved course, which
terminates in the middle of the field, all three horses arriving there
together.
The horses obviously ran at the same speed, but just how far did they
run?

Explanation

Exactly 100 yards. This is because at any moment the horses are at the
vertices of an equilateral triangle which diminishes at the velocity of
the horses. Thus 100/V is the time it takes for the triangle to become a
point in the middle of the field. The distance the horses travel during
that time is V x 100/V which equals exactly 100 yards.